The invention relates to a device for the aerobic treatment, conditioning and/or drying of moist, preferably at least partly organic material essentially of a solid or paste-like nature, utilizing a specific reactor geometry and special inserts. The device is suitable in particular for the microbiological treatment, conditioning and/or hygienization of organic residues and other organic wastes, in particular of industrial and communal sewage sludges, and of wastes from agricultural production, large-scale animal keeping, horticulture and industrial production of food and of luxury consumables, for the purpose of long-term stabilization of the residues and/or for the production of organic and organo-mineral fertilizers, culture substrates and/or soil conditioners.